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        <h1 id="chapter-02-sets-and-relations">chapter 02 Sets and Relations</h1>
<p>部分作业答案</p>
<p><a href="https:/gitee.com/xingyongkang">邢永康</a></p>
<h2 id="p75-2">p75 (2)</h2>
<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>→</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>z</mi><mo stretchy="false">)</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>→</mo><mi mathvariant="normal">¬</mi><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>z</mi><mo stretchy="false">)</mo><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>→</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>→</mo><mi mathvariant="normal">¬</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∨</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>→</mo><mi mathvariant="normal">¬</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∨</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∨</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd class ="mtr-glue"></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∨</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∨</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 这是前束合取范式</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd class ="mtr-glue"></mtd><mtd class ="mml-eqn-num"></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∨</mo><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>∪</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∪</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>∨</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>∨</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∨</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mtext>也可以把（1）式看作是三个命题变量的主合取范式，快速写出它的主析取范式</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 0,0,0</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>∨</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 0,0,1</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>∨</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 0,1,0</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>∨</mo><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 0,1,1</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>∨</mo><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 1,0,0</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>∨</mo><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 1,0,1</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>∨</mo><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>∧</mo><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>∧</mo><mi mathvariant="normal">¬</mi><mi>R</mi><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mspace width="1em"/><mo stretchy="false">(</mo><mtext> 1,1,0</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mo stretchy="false" lspace="0em" rspace="0em">)</mo></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{align*}
&amp; (\forall x )(P(x) \rightarrow (\forall y)((\forall z)Q(x,y) \rightarrow \neg(\forall z)R(y,x))) \\
\iff &amp; (\forall x )(P(x) \rightarrow (\forall y)(Q(x,y) \rightarrow \neg(R(y,x))) \\
\iff &amp; (\forall x )(\neg P(x) \vee (\forall y)(Q(x,y) \rightarrow \neg(R(y,x)) ) \\
\iff &amp; (\forall x)(\neg P(x) \vee (\forall y)(\neg Q(x,y) \vee \neg R(y,x))) \\
\iff &amp; (\forall x)(\forall y)(\neg P(x) \vee \neg Q(x,y) \vee \neg R(y,x))  \quad \tag{1}(\text{ 这是前束合取范式}) \\
\iff &amp; (\forall x)(\forall y)(\neg P(x) \vee (Q(x,y) \wedge \neg Q(x,y)) \cup \neg Q(x,y) \cup \neg R(y,x) ) \\
\iff &amp; (\forall x)(\forall y)((\neg P(x) \wedge Q(x,y)) \vee (\neg P(x) \wedge \neg Q(x,y)) \vee \neg Q(x,y) \vee \neg R(y,x) ) \\
\iff &amp; ... \\
&amp; \text{也可以把（1）式看作是三个命题变量的主合取范式，快速写出它的主析取范式} \\
\iff &amp; (\forall x) (\forall y) (  \\ 
  &amp;(\neg P(x) \wedge \neg Q(x,y) \wedge \neg R(y,x))  \quad (\text{ 0,0,0})\\
  &amp;\vee (\neg P(x) \wedge \neg Q(x,y) \wedge R(y,x))  \quad (\text{ 0,0,1})\\
  &amp;\vee (\neg P(x) \wedge Q(x,y) \wedge \neg R(y,x))  \quad (\text{ 0,1,0})\\
  &amp;\vee (\neg P(x) \wedge Q(x,y) \wedge R(y,x))  \quad (\text{ 0,1,1})\\
  &amp;\vee (P(x) \wedge \neg Q(x,y) \wedge \neg R(y,x))  \quad (\text{ 1,0,0})\\
  &amp;\vee (P(x) \wedge \neg Q(x,y) \wedge R(y,x))  \quad (\text{ 1,0,1})\\
  &amp;\vee (P(x) \wedge Q(x,y) \wedge \neg R(y,x))  \quad (\text{ 1,1,0})\\ 
  )
\end{align*}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:27em;vertical-align:-13.25em;"></span><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:13.75em;"><span style="top:-15.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-14.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-12.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-11.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-9.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-8.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-6.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-5.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span><span style="top:-0.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:0.59em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:2.09em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:3.59em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:5.09em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:6.59em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:8.09em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:9.59em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:13.25em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:13.75em;"><span style="top:-15.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">((</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">¬</span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">)))</span></span></span><span style="top:-14.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">¬</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">)))</span></span></span><span style="top:-12.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">¬</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">)))</span></span></span><span style="top:-11.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">)))</span></span></span><span style="top:-9.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> </span><span class="mord cjk_fallback">这是前束合取范式</span></span><span class="mclose">)</span></span></span><span style="top:-8.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">))</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span></span></span><span style="top:-6.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">((</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">))</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">))</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span></span></span><span style="top:-5.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mord">...</span></span></span><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mord text"><span class="mord cjk_fallback">也可以把（</span><span class="mord">1</span><span class="mord cjk_fallback">）式看作是三个命题变量的主合取范式，快速写出它的主析取范式</span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">∀</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mopen">(</span></span></span><span style="top:-0.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> 0,0,0</span></span><span class="mclose">)</span></span></span><span style="top:0.59em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> 0,0,1</span></span><span class="mclose">)</span></span></span><span style="top:2.09em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> 0,1,0</span></span><span class="mclose">)</span></span></span><span style="top:3.59em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> 0,1,1</span></span><span class="mclose">)</span></span></span><span style="top:5.09em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> 1,0,0</span></span><span class="mclose">)</span></span></span><span style="top:6.59em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> 1,0,1</span></span><span class="mclose">)</span></span></span><span style="top:8.09em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∨</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">Q</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∧</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">¬</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">))</span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord"> 1,1,0</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:11.75em;"><span></span></span></span></span></span></span></span><span class="tag"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:13.75em;"><span style="top:-15.91em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-14.41em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-12.91em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-11.41em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-9.91em;"><span class="pstrut" style="height:3em;"></span><span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">1</span></span><span class="mord">)</span></span></span></span><span style="top:-8.41em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-6.91em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-5.41em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:-0.91em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:0.59em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:2.09em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:3.59em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:5.09em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:6.59em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:8.09em;"><span class="pstrut" style="height:3em;"></span><span></span></span><span style="top:9.59em;"><span class="pstrut" style="height:3em;"></span><span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:13.25em;"><span></span></span></span></span></span></span></span></span></p>

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